Write each of the following in the simplest form:

Put x = tanθ

⇒ θ = tan^{–1}(x)

tan^{–1}{tanθ +}

= tan^{–1}{tanθ +}

= tan^{–1}{tanθ +secθ }

= tan^{–1}

= tan^{–1}

Sinθ = ,cosθ =

= tan^{–1}

= tan^{–1}

= tan^{–1}

Dividing by we get,

= tan^{–1}

= tan^{–1}

= tan^{–1}

tan(x+y) =

= tan^{–1}

=

From 1 we get

= ^{.}

Therefore, the simplification of given equation is ^{.}

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